{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9 - Clustering\n",
    "\n",
    "1 - Aplique os algoritmos K-means [1] e AgglomerativeClustering [2], experimentando as medidas de distância disponíveis. Compare os resultados, utilizando métricas de avaliação de clusteres (completeness e homogeneity, por exemplo) [3].\n",
    "\n",
    "* [1] http://scikit-learn.org/stable/modules/clustering.html#k-means\n",
    "\n",
    "* [2] http://scikit-learn.org/0.17/modules/clustering.html#hierarchical-clustering\n",
    "\n",
    "* [3] http://scikit-learn.org/stable/modules/clustering.html#clustering-evaluation\n",
    "\n",
    "2 - Aplique o Método da Silhueta (Utilize silhouette_score [4] e/ou silhouette_samples [5]) em relação aos resultados do algoritmo K-means. Observe o resultado da avaliação (entenda as saídas dos métodos, conforme referências abaixo) e identifique a qualidade da sua clusterização. \n",
    "\n",
    "* [4] http://scikit-learn.org/0.17/modules/generated/sklearn.metrics.silhouette_score.html#sklearn.metrics.silhouette_score\n",
    "\n",
    "* [5] http://scikit-learn.org/0.17/modules/generated/sklearn.metrics.silhouette_samples.html#sklearn.metrics.silhouette_samples\n",
    "\n",
    "3 - Qual o valor de K (número de clusteres) você escolheu para a questão anterior? Desenvolva o Método do Cotovelo (não utilizar lib!) e descubra o K mais adequado. Após descobrir, aplique novamente o K-means com o K adequado. \n",
    "\n",
    "* Ajuda: atributos do [k-means](http://scikit-learn.org/0.17/modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans)\n",
    "\n",
    "4 - Após a questão 3, você aplicou o algoritmo com K apropriado. Refaça a questão 2 de acordo com os resultados de clusters obtidos com a questão anterior e verifique se o resultado melhorou.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import decomposition\n",
    "from sklearn import metrics\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from sklearn.cluster import KMeans\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "dataset = load_iris()\n",
    "X = dataset.data\n",
    "y = dataset.target\n",
    "\n",
    "def PlotClusters(reduced_data_df, clustering):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.scatter(reduced_data_df[0], reduced_data_df[1], c=clustering)\n",
    "    plt.show()\n",
    " # Original   \n",
    "def PlotOrig(reduced_data_df, y):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.scatter(reduced_data_df[0], reduced_data_df[1], c=y)\n",
    "    plt.show()\n",
    "    return\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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h7Y5dldZaU8X8o6AJwcvnjGTdwQMs3rOb1Lg4hrdui9seehtoFJ/AvpxI4bYG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\nCUiLv1JKJaD/B10mSWyNIj9xAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4bd00b3dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZlLJ34b/J1b1vvPnwsS/wuiIdP4Ar18WDw56qNxs/ioZFntfLiE8/5LM1q9lXkM/Wg9k8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\nrMpELogAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4bd00b3080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans = KMeans(n_clusters=3, random_state=0).fit(X)\n",
    "predictions = kmeans.predict(X)\n",
    "reduced_data = decomposition.PCA(n_components=2).fit_transform(X)\n",
    "reduced_data_df = pd.DataFrame(reduced_data)\n",
    "reduced_data_df[2] = predictions\n",
    "\n",
    "PlotClusters(reduced_data_df, reduced_data_df[2])\n",
    "# Original\n",
    "PlotOrig(reduced_data_df, y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iyz/jdLiQHg8mi4k2fVvw8g9Pp90AJrz8E79//pff5qnQCQxGPTpNh5TQoH0d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\nGFOErPgbY0wRsuJvjDFF6P8B3sfKp6o48mAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4bd021a0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZlLJ34b/J1b1vvPnwsS/wuiIdP4Ar18WDw56qNxs/ioZFntfLiE8/5LM1q9lXkM/Wg9k8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\nrMpELogAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4bd0261a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "agglo = AgglomerativeClustering(n_clusters=3, affinity=\"euclidean\", linkage=\"complete\").fit_predict(X)\n",
    "\n",
    "PlotClusters(reduced_data_df, agglo)\n",
    "# Original\n",
    "PlotOrig(reduced_data_df, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Jjoq17jRDzfwj4bwYHGcSlGewB6UaRBIiZXxwuRypgbu+u2hJLj0zMA6ej7G/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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4bc38cf4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZlLJ34b/J1b1vvPnwsS/wuiIdP4Ar18WDw56qNxs/ioZFntfLiE8/5LM1q9lXkM/Wg9k8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\nrMpELogAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4bc3b35198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "agglo_Manhattan = AgglomerativeClustering(n_clusters=3, affinity=\"manhattan\", linkage=\"complete\").fit_predict(X)\n",
    "\n",
    "\n",
    "\n",
    "PlotClusters(reduced_data_df, agglo_Manhattan)\n",
    "\n",
    "# Original\n",
    "PlotOrig(reduced_data_df, y)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vXjSE5bfeyfwxYxnT6RzunDGNWTt3hD3ftCT9Ev5ZC5DiyuGVRQtwmyZ+KZGA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\nvzHGpKD/B9CePIT4iH/IAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4bc37f3470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZlLJ34b/J1b1vvPnwsS/wuiIdP4Ar18WDw56qNxs/ioZFntfLiE8/5LM1q9lXkM/Wg9k8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\nDQijKzjORQjVie5Ip8E5f4vVQAgRWcw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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4bc37f3c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "agglo_Cosine = AgglomerativeClustering(n_clusters=3, affinity=\"cosine\", linkage=\"complete\").fit_predict(X)\n",
    "PlotClusters(reduced_data_df, agglo_Cosine)\n",
    "# Original\n",
    "PlotOrig(reduced_data_df, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K-Means Metrics \n",
      " Homogeneity: 0.751485402199 \n",
      " Completeness: 0.764986151449 \n",
      "\n",
      "Agglomerative Clustering Metrics - Euclidean \n",
      " Homogeneity: 0.700115437096 \n",
      " Completeness: 0.745438275302 \n",
      "\n",
      "Agglomerative Clustering Metrics - Manhattan \n",
      " Homogeneity: 0.778176865951 \n",
      " Completeness: 0.803588540623 \n",
      "\n",
      "Agglomerative Clustering Metrics - Cosine \n",
      " Homogeneity: 0.717058965034 \n",
      " Completeness: 0.773421193274\n"
     ]
    }
   ],
   "source": [
    "#Metrics\n",
    "\n",
    "#Kmeans\n",
    "metric_Kmeans_homo = metrics.homogeneity_score(y, reduced_data_df[2])\n",
    "metric_Kmeans_comp = metrics.completeness_score(y, reduced_data_df[2]) \n",
    "\n",
    "#Agglomerative - Euclidean\n",
    "metric_AggloEuclidean_homo = metrics.homogeneity_score(y, agglo)\n",
    "metric_AggloEuclidean_comp = metrics.completeness_score(y, agglo) \n",
    "\n",
    "#Agglomerative - Manhattan\n",
    "metric_AggloManhattan_homo = metrics.homogeneity_score(y, agglo_Manhattan)\n",
    "metric_AggloManhattan_comp = metrics.completeness_score(y, agglo_Manhattan) \n",
    "\n",
    "#Agglomerative - Cosine\n",
    "metric_AggloCosine_homo = metrics.homogeneity_score(y, agglo_Cosine)\n",
    "metric_AggloCosine_comp = metrics.completeness_score(y, agglo_Cosine) \n",
    "\n",
    "print (\"K-Means Metrics \\n Homogeneity:\", metric_Kmeans_homo, \"\\n Completeness:\", metric_Kmeans_comp, \"\\n\")\n",
    "print (\"Agglomerative Clustering Metrics - Euclidean \\n Homogeneity:\", metric_AggloEuclidean_homo, \"\\n Completeness:\", metric_AggloEuclidean_comp, \"\\n\")\n",
    "print (\"Agglomerative Clustering Metrics - Manhattan \\n Homogeneity:\", metric_AggloManhattan_homo, \"\\n Completeness:\", metric_AggloManhattan_comp, \"\\n\")\n",
    "print (\"Agglomerative Clustering Metrics - Cosine \\n Homogeneity:\", metric_AggloCosine_homo, \"\\n Completeness:\", metric_AggloCosine_comp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lBeu21VZw0UUwceKGN7mtWgWnnFJMXGY2aJwUbH0SPPVU5W1Ll8L3vpcezawp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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4bc3863780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Metodo do Cotovelo\n",
    "from scipy.spatial.distance import cdist\n",
    "\n",
    "distortions = []\n",
    "K = range(1,10)\n",
    "for k in K:\n",
    "    kmeanModel = KMeans(n_clusters=k).fit(X)\n",
    "    kmeanModel.fit(X)\n",
    "    distortions.append(sum(np.min(cdist(X, kmeanModel.cluster_centers_, 'euclidean'), axis=1)) / X.shape[0])\n",
    "\n",
    "# Plot the elbow\n",
    "plt.plot(K, distortions, 'ro-')\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('Distortion')\n",
    "plt.title('The Elbow Method showing the optimal k')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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88gxmv1SDiEXEjfO/Lodr4O47kBuLlc556MduQD/SHP3Y9Ujn3HIzX3F6sWL2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\nFX9jjMlAVvyNMSYD/T8rWEaAFXbL8QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4bd01e6ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZlLJ34b/J1b1vvPnwsS/wuiIdP4Ar18WDw56qNxs/ioZFntfLiE8/5LM1q9lXkM/Wg9k8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\nrMpELogAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4bc3b35ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeansOptimal = KMeans(n_clusters=2).fit(X)\n",
    "predictions = kmeansOptimal.predict(X)\n",
    "\n",
    "PlotClusters(reduced_data_df, predictions)\n",
    "\n",
    "# Original\n",
    "PlotOrig(reduced_data_df, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
